


In this study, by attempting to resolve the angular complication during the particle generation for the muon tomography applications in the GEANT4 simulations, we exhibit an unconventional methodology that is hinged on the direction limitation via the vectorial construction from the generation location to the restriction area rather than using a certain angular distribution or interval. In other words, we favor a momentum direction that is determined by a vector constructed between an initial point randomly chosen on a generative point/plane and a latter point arbitrarily selected on a restrictive plane of the same dimensions with the basal cross section of the volume-of-interest (VOI). On account of setting out such a generation scheme, we optimize the particle loss by keeping an angular disparity that is directly dependent on the VOI geometry as well as the vertical position of the restrictive plane for a tomographic system of a finite size. We demonstrate our strategy for a set of target materials including aluminum, copper, iron, lead, and uranium with a dimension of 40\(\times \) 10\(\times \) 40 \(\rm cm^{3}\)  over three restrictive planes of different positions by using a discrete energy spectrum between 0.1 and 8 GeV and we compute the scattering angle, the number of absorption, and the particle loss. Upon our simulation outcomes, we show that the particle generation by means of restrictive planes is an effective strategy that is flexible towards a variety of computational objectives in the GEANT4 simulations.

Keywords:  Muon tomography; Characteristic parameters; Restrictive planes; Source biasing; Non-analogue Monte Carlo simulations; GEANT4
section1-2.5ex plus-1ex minus-.2ex2.3ex plus.2exIntroduction
The wide angular distribution [1]} of the incoming cosmic ray muons in connection with either incident angle or azimuthal angle is a challenging trait that leads to a drastic particle loss in the course of parametric computations through the GEANT4 [2]} simulations associated with the muon tomography [3]}, [4]}, [5]} since the tomographic configurations as well as the target geometries also influence the processable number of the detected particles apart from the generation strategies. To further detail, the basic parameters such as the scattering angle, the particle displacement, and the particle absorption owing to the volume-of-interest (VOI) de facto dictate the particle penetration through the multiple sections of the tomographic setup in addition to the VOI. Hence, a number of the loss cases notably come into effect unless the calculation conditions are fulfilled, and not only the computation statistics as well as the numerical outcomes but the initial assumptions like the energy spectrum are also perturbed since the VOI accepts a significantly lower number of particles in the instance of the substantial particle loss. While a number of source biasing techniques [6]} are offered by MCNP6 [7]}, [8]} in the black box format under the class of non-analogue Monte Carlo simulations, the GEANT4 simulations are usually constrained to the existing particle generators or the general particle source (GPS) unless G4ParticleGun is favored. Motivated by the excessive particle loss and its effect on the computation time as well as the characteristic parameters identified in the muon tomography, we set forth in the present study a scheme that is hinged on the particle generation through the planar restriction by means of the vectorial construction over our tomographic setup consisting of plastic scintillators manufactured from polyvinyl toluene with the dimensions of 100\(\times \) 0.4\(\times \) 100 \(\rm cm^{3}\) . This study is organized as follows. In section REF , we elucidate our methodology based on the restrictive planes and we express our characteristic parameters as well as our simulation features in section REF . While we disclose our simulation outcomes in section REF , we draw our conclusions in section REF .
section1-2.5ex plus-1ex minus-.2ex2.3ex plus.2exGeneration via planar restriction

To begin with, we principally exhibit two planar restrictive schemes to be adapted in GEANT4 as illustrated in Fig. REF  where (a) shows the particle generation from a fixed point as well as the direction restriction by means of a restrictive pseudo-plane, whereas (b) demonstrates the randomly picked up particles from a generative plane, the directions of which are projected into a similar restrictive plane.
<FIGURE>